Solve Vo: Voltage Nodal Analysis w/ KCL Equation

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Discussion Overview

The discussion revolves around solving for the voltage Vo using voltage nodal analysis and Kirchhoff's Current Law (KCL) in a circuit involving dependent sources. Participants are examining the formulation of the KCL equation and the implications of node labeling.

Discussion Character

  • Homework-related, Technical explanation

Main Points Raised

  • One participant questions whether the dependent voltage source 20iΔ should be considered negative in the KCL equation for node Vb, based on the direction of current flow.
  • Another participant points out the absence of a label for Vo in the original post and seeks clarification on which voltage is intended to be solved.
  • A later reply confirms that Vo is equivalent to Vb, as it is labeled across the 40-ohm resistor.
  • One participant agrees with the formulation of the KCL equation and notes that the voltage at node Vc is negative due to the polarity of the dependent source.

Areas of Agreement / Disagreement

Participants express some agreement on the formulation of the KCL equation, but there remains uncertainty regarding the treatment of the dependent voltage source and the labeling of Vo.

Contextual Notes

There are unresolved questions about the assumptions regarding current direction and node labeling, which may affect the analysis.

elhaxx
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I'm asked to solve for Vo for this equation. I've set the bottom node to be my reference node before applying nodal analysis. When included in the KCL equation for node at Vb, will the dependent voltage source 20iΔ be negative since the current through that element is leaving node C?
Say, the equation would be: [(Vb-10v)/10Ω]+ (Vb/40Ω)+[(Vb+20iΔ)/20Ω]=0
Thanks!
 
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I moved this to the homework forum. Please post homework questions to a homework forum and fill out the required information.
 
elhaxx said:
When included in the KCL equation for node at Vb, will the dependent voltage source 20iΔ be negative since the current through that element is leaving node C?

–20iΔ is the voltage Vc

(typo corrected)
 
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Welcome to the PF.
elhaxx said:
I'm asked to solve for Vo for this equation.
I see Va, Vb, Vc labeled, but no Vo label. Which voltage are you supposed to solve for? Thanks.
 
berkeman said:
Welcome to the PF.

I see Va, Vb, Vc labeled, but no Vo label. Which voltage are you supposed to solve for? Thanks.
Vo = Vb, labeled across the 40ohm resistor.
 
Your equation looks good to me. The voltage at node Vc is negative because of the polarity of the dependent source, as labeled in the schematic.
 
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